The medium of chat is descended from talk, but the terms (and the media) have been distinct since at least the early 1990s. talk is prototypically for a small number of people, generally with no provision for channels. In chat systems, however, there are many channels in which any number of people can talk; and users may send private (one-to-one) messages.
Chat systems have given rise to a distinctive style combining the immediacy of talking with all the precision (and verbosity) that written language entails. It is difficult to communicate inflection, though conventions have arisen to help with this.
The conventions of chat systems include special items of jargon, generally abbreviations meant to save typing, which are not used orally. E.g. BCNU, BBL, BTW, CUL, FWIW, FYA, FYI, IMHO, OT, OTT, TNX, WRT, WTF, WTH, <g>, <gr&d>, BBL, HHOK, NHOH, ROTFL, AFK, b4, TTFN, TTYL, OIC, re.
Much of the chat style is identical to (and probably derived from) Morse code jargon used by ham-radio amateurs since the 1920s, and there is, not surprisingly, some overlap with TDD jargon. Most of the jargon was in use in talk systems. Many of these expressions are also common in Usenet news and electronic mail and some have seeped into popular culture, as with emoticons.
The MUD community uses a mixture of emoticons, a few of the more natural of the old-style talk mode abbreviations, and some of the "social" list above. In general, though, MUDders express a preference for typing things out in full rather than using abbreviations; this may be due to the relative youth of the MUD cultures, which tend to include many touch typists. Abbreviations specific to MUDs include: FOAD, ppl (people), THX (thanks), UOK? (are you OK?).